Abstract

Graph coloring is used to characterize some properties of graphs. A b-coloring of a graph G (using colors 1,2,...,k) is a coloring of the vertices of G such that (i) two neighbors have different colors (proper coloring) and (ii) for each color class there exists a dominating vertex which is adjacent to all other k-1 color classes. In this paper, based on a b-coloring of a graph, we propose a new clustering technique. Additionally, we provide a cluster validation algorithm. This algorithm aims at finding the optimal number of clusters by evaluating the property of color dominating vertex. We adopt this clustering technique for discovering a new typology of hospital stays in the French healthcare system.